List of top Atmospheric Science Questions asked in CUET (PG)

\[\begin{array}{|c|c|} \hline \textbf{Class interval} & \textbf{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 15 \\ 15-20 & 22 \\ 20-25 & 25 \\ 25-30 & 10 \\ 30-35 & 3 \\ \hline \end{array}\]

The differential equation \( (1+3x^2y^2+\beta x^2y^4)dx + (2x^3y+2x^3y^3)dy = 0 \) will be exact differential equation if (assuming typos in original question are corrected as shown):

Let \((\alpha, \beta)\) be the centre and \(\gamma\) be the radius of the circle \(x^2+y^2-6x-2y-15=0\), then the value of \((\alpha^2+\beta^2+\gamma^2)\) is:

In a sports event of football and basketball, 132 students registered to play football and 93 students registered in basketball. If the total number of students registered in the event is 200, then the number of students registered in both the games is:

The imaginary part of the complex number \( \log(1+i) \) is

Let \( g(x) = x^2 \), \( -\pi \le x \le \pi \). The coefficient of \( \cos(3x) \) in the Fourier series expansion of \(g(x)\) is:

Let \(y(t)\) be the solution of the differential equation \(y''+4y=0\), \(y(0)=1\), \(y'(0)=-6\), then the Laplace transformation \(Y(s)\) of the solution is equal to

Match LIST-I with LIST-II
LIST-I (Differential Equation)
(A) \(\frac{dy}{dx} = 2x(y-x^2+1)\)
(B) \(x\frac{dy}{dx} + 2(x^2+1)y=6\)
(C) \((x^2+1)\frac{dy}{dx} + 2xy = x \sin x\)
(D) \(x^3\frac{dy}{dx} + 2xy = 2x^2e^{x^2}\)
LIST-II (Integrating Factor)
(I) \(x^2\)
(II) \(e^{-x^2}\)
(III) \(x^2e^x\)
(IV) \(1+x^2\)
Choose the correct answer from the options given below:

Which of the following statements are correct?
A. In a skew-symmetric matrix, all diagonal elements are zero.
B. A square matrix is called a diagonal matrix if all its non-diagonal elements are one.
C. If the determinant of the matrix is zero, then the matrix is known as non-singular matrix.
D. The product of a matrix A and its adjoint is equal to unit matrix multiplied by the determinant A.

If \(f(t)\) is the inverse Laplace transform of \( F(s) = \frac{s+1+s^{-2}}{s^2-1} \), then \(f(t)\) is

If \( A = \begin{bmatrix} 1 & 2 & -1 \\ 3 & 4 & 2 \\ 2 & 0 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 1 & 3 \\ -4 & 0 \\ 2 & 5 \end{bmatrix} \) are two matrices, then which one of the following is incorrect: